Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
Abstract
We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. A result of N.J. Kalton is included which shows that this is best possible in that: A frame can be represented as a linear combination of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple of a) sum of two normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1998
 DOI:
 10.48550/arXiv.math/9811148
 arXiv:
 arXiv:math/9811148
 Bibcode:
 1998math.....11148C
 Keywords:

 Mathematics  Functional Analysis;
 46B20;
 46C05
 EPrint:
 to appear: J. of Fourier Anal. and Appl's